Ratio, Proportion and Percentages Formulas and Tricks
Ratio & Proportion

The equality of two ratios is called a proportion. If , we write and we say that a, b, c, d are in proportion. In a proportion, the first and fourth terms are known as extremes, while the second and third are known as means.


Mean proportion between a and b is

The compounded ratio of the ratios is

is a duplicate ratio of

is a subduplicate ration of

is a triplicate ratio of

is a subtriplicate ratio of

If , then , which is called the Componendo.

If , which is called the dividendo

If , which is called the componendo & dividendo.

Variation: We say that x is directly proportional to y if for some constant k and we write,

Also, we say that x is inversely proportional to y for some constant k and we write
Ratios


If then for a positive quantity x,

If then for a positive quantity x,

Proportions
Percentage

To express x% as a fraction, we have

To express as a percent, we have

If ‘A’ is R% more than ‘B’, then ‘B’ is less than ‘A’ by
OR
If the price of a commodity increases by R%, then the reduction in consumption, not to increase the expenditure is

If ‘A’ is R% less than ‘B’, then ‘B’ is more than ‘A’ by
OR
If the price of a commodity decreases by R%, then the increase in consumption, not to increase the expenditure is

If the population of a town is ‘P’ in a year, then its population after ‘N’ years is

If the population of a town is ‘P’ in a year, then its population ‘N’ years ago is
Percentage Change


For two successive changes of and